This paper asks whether phenomenal intentionality (intentionality that arises from phenomenal consciousness alone) has a relational structure of the sort envisaged in Russell’s theory of acquaintance. I put forward three arguments in favor of a relational view: one phenomenological, one linguistic, and one based on the view’s ability to account for the truth conditions of phenomenally intentional states. I then consider several objections to the relational view. The chief objection takes the form of a dilemma between Platonic and Aristotelian conceptions of the properties constitutive of the contents of phenomenal intentional states on this view: the Aristotelian view seems unable to account for all the apparent contents of phenomenal intentional states, but the Platonic view seems to be ontologically unacceptable. I also consider other objections from physicalism, phenomenology, and epistemology.